On the nonlinear stability of higher dimensional triaxial Bianchi-IX black holes

Mihalis Dafermos, Gustav Holzegel

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


In this paper, we prove that the five-dimensional Schwarzschild- Tangherlini solution of the Einstein vacuum equations is orbitally stable (in the fully non-linear theory) with respect to vacuum perturbations of initial data preserving triaxial Bianchi-IX symmetry. More generally, we prove that five-dimensional vacuum spacetimes developing from suitable asymptotically flat triaxial Bianchi-IX symmetric initial data and containing a trapped or marginally trapped homogeneous 3-surface necessarily possess a complete null infinity I+, whose past J-(I+) is bounded to the future by a regular event horizon H+, whose cross-sectional volume in turn satisfies a Penrose inequality, relating it to the final Bondi mass. In particular, the results of this paper give the first examples of vacuum black holes which are not stationary exact solutions.

Original languageEnglish (US)
Pages (from-to)503-523
Number of pages21
JournalAdvances in Theoretical and Mathematical Physics
Issue number4
StatePublished - Aug 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Physics and Astronomy


Dive into the research topics of 'On the nonlinear stability of higher dimensional triaxial Bianchi-IX black holes'. Together they form a unique fingerprint.

Cite this